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Einstein's Field Equations

These equations relate the geometry of spacetime (represented by the Einstein tensor G) to the energy-momentum tensor T, describing gravity's effect.

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The statement of the theorem

Define the Einstein tensor

G_{\mu\nu}

G_{\mu\nu} = R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R

, where

R_{\mu\nu}

is the Ricci curvature tensor and

R

is the Ricci scalar. The field equations relate this geometric tensor to the energy-momentum tensor

T_{\mu\nu}

via:\n\n

G_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}

\n\nHere,

g_{\mu\nu}

is the metric tensor,

G

is Newton's gravitational constant, and

c

is the speed of light.

Source: Wikipedia